New forms of mathematical knowledge are growing in importance for mathematics and education, including tacit knowledge, knowledge of particulars, language, and rhetoric in mathematics. Highlights the importance of attending to rhetoric and the range of rhetorical styles in school mathematics, and the need for explicit instruction in this area.…

This paper contains the comments of a discussant reviewing the paper, "The Role of Visual Representations in the Learning of Mathematics" (Abraham Arcavi). A research-based evaluation is made that focuses on the ideas of stochastics and the epistemological triangle. (Contains 28 references.) (DDR)

As biological and socio-cultural beings, humans are encouraged and aspire to "see" not only what comes "within sight," but also what is not possible to see. Visualization is described as offering a method of seeing the unseen. These ideas are organized into sections that focus on seeing the unseen in data, seeing the unseen in…

This paper gives a brief introduction to a discipline called the cognitive science of mathematics. The theoretical background of the arguments is based on embodied cognition and findings in cognitive linguistics. It discusses Mathematical Idea Analysis, a set of techniques for studying implicit structures in mathematics. Particular attention is…

This paper focuses on some cognitive and didactical phenomena that feature processes and products of pupils in grades 7-12 who learned mathematical proof within technological environments. The main issues in the analysis of students' performances consist of metaphors, deictics, mental times, narratives, functions of dragging, abductions, and…

Provides information about hypnosis. Uses research data to define hypnosis, discuss the relationship between hypnosis and memory, and present some possible benefits. Includes a chart with some common misconceptions about hypnosis and the corresponding true statement. (DDR)

An appreciation of the relationship between novice and expert knowledge frameworks may help develop an understanding of the process of transition from one to the other. Recommends the use of concept mapping. (DDR)

Argues that the organization of cognitive structures for technical domains can be visualized as a network of connected thinkable models. Describes a taxonomy of models that has been developed and discusses the issue of how representations relate to human modes of perception and action. Contains 25 references. (DDR)

This paper suggests that the systems of representations that we use in mathematics have a cultural origin and concludes that the knowledge produced with the help of these systems of representation likewise has a cultural origin. This assertion forces a reformulation of the issue of objectivity in terms that differ from those inherited from…

Reports research that examines children's models of seed. Explores the conceptions held by children (N=75) of germination and seed formation. Concludes that children hold a restricted meaning for the term 'seed'. (DDR)

Identifies certain conceptions regarding the science content studied by students aged 9-11 years and develops a strategy for altering these conceptions. Reviews research on misconceptions and defines action research. (DDR)

Determines teachers' conceptions of evolutionary theory using the technique of concept mapping. Discusses the methodology, the survey items, and concept map features. Makes specific recommendations for the teaching of evolution. (Contains 32 references.) (DDR)

Describes six divergent forms of constructivism in providing an overview of constructivist theory. Suggests a scheme for characterizing constructivist writing on the basis of its relative emphasis on personal versus social construction of knowledge, and objectivist versus relativist views of the nature of science. Contains 31 references. (DDR)

Argues that some forms of constructivism propose an epistemological idealism with a concomitant relativism, while other forms are explicitly opposed to such positions. Explains that all forms of constructivism are often presented as being relativistic. Contains 31 references. (DDR)

Examines central parts from the first two papers in this journal by Peter Slezak criticizing the "sociology of scientific knowledge". Considers some of the main philosophical issues raised by sociologists of science. Contains 87 references. (DDR)